Specifically, we employ a directed acyclic graph neural network (DAGNN)
[1]} to encode DAG information in a set of embedding
vectors and incorporate the partial order relationship in the DAG
into the neural network. However, DAGNN uses an iterative message
passing scheme which is computationally expensive. Consequently, we
propose a Pipeline Mechanism to speed up the feature extraction process,
namely Pipelined-DAGNN. After Pipelined-DAGNN processing, we feed
the embedding sequence of schedulable coflows to the self-attention
layer for information interaction, where a schedulable coflow is one
that has no predecessor dependencies or all its preceding flows have
been scheduled. The output self-attentive sequence serves as the input
of the policy network to generate a priority scheduling list. The
self-attention mechanism is the key for ensuring the accuracy of the
scheduling policy. Based on the list, flows in each coflow is further
scheduled in a fine-grained fashion. In our multi-stage job scheduling
problem, information about the future jobs is not known. Therefore,
our scheduling algorithm is online, which consists of coflow ordering
and scheduling two parts. See Section  for details.
